Two particles have equal kenetic energies

In summary, the answer is no, having equal kinetic energies does not necessarily mean having the same momentum. This is because momentum is determined by both mass and velocity, while kinetic energy is only determined by mass and velocity squared. Additionally, for particles with high speeds, the relativistic expression for kinetic energy should be used instead of the Newtonian one.
  • #1
napier212121
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0
if two particles have equal kenetic energies, do they have the same momentum?
 
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  • #2
NO! Just because something has the same kinetic energy doesn't mean it has the same momentum. There are a number of factors that could affect it.
 
  • #3
Kinetic energy of an object with mass m and velocity v is (1/2)mv2. Momentum is mv.

Take for example, an object with mass 4kg and speed 1 m/s. Its kinetic energy is (1/2)(4)(1)2= 2 Joules and its momentum is (4)(1)= 4 kgm/s. Take a second object with mass 1kg and speed 2 m/s. It has kinetic energy (1/2)(1)(2)2= 2 Joules also but its momentum is (1)(2)= 2 kgm/s.
 
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  • #4
Originally posted by HallsofIvy
Kinetic energy of an object with mass m and velocity v is (1/2)mv<sup>2</sup>. Momentum is mv.

Take for example, an object with mass 4kg and speed 1 m/s. Its kinetic energy is (1/2)(4)(1)<sup>2</sup>= 2 Joules and its momentum is (4)(1)= 4 kgm/s. Take a second object with mass 1kg and speed 2 m/s. It has kinetic energy (1/2)(1)(2)<sup>2</sup>= 2 Joules also but its momentum is (1)(2)= 2 kgm/s.

Well, kinetic energy (for particles, as the question originally asked) is probably more likely to be [itex] K = (\gamma - 1) mc^2[/itex], i.e. relativistic kinetic energy, which reduces to the Newtonian expression in the limit of small v.
 

1. What does it mean for two particles to have equal kinetic energies?

When two particles have equal kinetic energies, it means that they are moving at the same speed, regardless of their mass or direction of motion.

2. How is kinetic energy calculated for two particles?

Kinetic energy is calculated by multiplying the mass of the particle by the square of its velocity. For two particles, this equation would be KE1 = 1/2mv12 and KE2 = 1/2mv22, where m is the mass and v is the velocity of each particle.

3. Can two particles with different masses have equal kinetic energies?

Yes, two particles with different masses can have equal kinetic energies if their velocities are also different. For example, a heavier particle moving at a slower speed can have the same kinetic energy as a lighter particle moving at a faster speed.

4. What other factors can affect the kinetic energy of two particles?

The only factors that affect the kinetic energy of two particles are their mass and velocity. Other factors such as the particles' positions, direction of motion, or external forces do not impact their kinetic energy.

5. How does the conservation of energy relate to two particles having equal kinetic energies?

The law of conservation of energy states that energy cannot be created or destroyed, only transferred or converted between different forms. In the case of two particles with equal kinetic energies, the total kinetic energy of the system remains constant, demonstrating the conservation of energy.

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